The invention is based on a hydraulic circuit of a fuel injection system. A hydraulic circuit is already known in which a separate tie line branches off from the fuel supply line to each of the injection valves, and the fuel not injected is carried from each of the fuel injection valves to a fuel return line. There is no assurance that each fuel injection valve will be supplied well enough with fuel that reliable engine starting is attained by means of rapid flushing out of the vapor bubbles from the injection valves and cooling down of the heated fuel injection valves, especially in a so-called hot start, in which fuel is present in vapor form in the fuel lines and in the individual fuel injection valves.